基于混合Kalman椭圆拟合的移相干涉测量算法

Phase-shifting interferometry algorithm based on hybrid Kalman ellipse fitting

  • 摘要: 基于李萨如图的椭圆拟合(Lissajous ellipse fitting, LEF)算法,可以从移相干涉图中恢复物体表面三维形貌信息。由于孤立点、噪声和短弧拟合等因素影响,常用椭圆拟合算法精度受限,稳定性不高,因此提出了一种混合Kalman椭圆拟合算法。从固定或随机移相干涉图中计算得到两组符合李萨如图形简谐运动方程参数,将其作为混合Kalman椭圆拟合初始值,通过迭代得到椭圆参数的置信区间,从而确定最佳系数,求解出包裹相位。将三步、四步LEF的结果与移相公式法进行对比,分析了不同椭圆拟合算法的优劣。当移相量为随机值时,三步LEF误差RMS值为0.052 4 rad,比公式法减小了20.36%。当移相量为90°时,三步LEF误差RMS值为0.045 8 rad,比公式法减小了30.39%,四步LEF误差则与公式法相近。仿真与实验表明,该算法稳定性更好、性能优于其他拟合算法。

     

    Abstract: Based on the Lissajous ellipse fitting (LEF) algorithm, the 3D morphology information of the object surface can be recovered from the phase-shifting interferograms. Due to the influence of outliers, noise and short arc fitting, the commonly-used ellipse fitting algorithm is limited in accuracy and stability. Therefore, a hybrid Kalman ellipse fitting algorithm was proposed. Two sets of simple harmonic motion equation parameters conforming to Lissajous pattern were calculated from fixed or random phase-shifting interferograms, which were used as the initial values of hybrid Kalman ellipse fitting. The confidence intervals of ellipse parameters were obtained by iteration, and the optimal coefficient was determined to solve the wrapped phase. The results of three-step and four-step LEF were compared with that of phase-shifting formula method, and the advantages and disadvantages of different ellipse fitting algorithms were analyzed. When the phase shift is a random value, the RMS value of the three-step LEF error is 0.052 4 rad, which is 20.36% lower than that of the formula method. When the phase shift is 90°, the RMS value of the three-step LEF error is 0.045 8 rad, which is 30.39% lower than that of the formula method, and the four-step LEF error is similar to the formula method. Simulation and experiments show that the proposed algorithm has better stability and performance than other fitting algorithms.

     

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